Landmarking Protocol 3d3 + Hypothesis Viz

Landmarking protocol 3d3 (LM3d3) represents a significant advancement from LM3d1 (Selden Jr., Dockall, and Dubied 2020) and LM3d2 protocols that were developed to analyse Gahagan bifaces, which evolved from a 2D study (Selden Jr., Dockall, and Shafer 2018). Like LM3d1 and LM3d2, LM3d3 uses the mesh topology as the foundation for additional components of reference geometry, further expanding upon the previous landmarking protocols. The result is a landmarking protocol that provides for the improved characterisation of whole-object morphology, which can also be subset to explore morphological variation in plan, profile, and cross-section morphology. It also provides those data points needed to investigate questions of directional asymmetry, differences in front/back morphology, and morphological integration between blade and basal morphology.

knitr::include_graphics('images/landmarks.png')

Landmarks from LM3d1 serve as the basis for LM3d3.

Like its’ predecessors, LM3d3 was initially designed using the digit3DLand package in R. When the draft protocol was complete, it shifted to Geomagic Design X (Build Version 2020.0.1 [Build Number: 30]), where the workflow was modified to include those elements of reference geometry that articulate with the specific design attributes of each point.

The goal of this effort was to increase both the precision and rigour of the study by including the Z-dimension to capture morphological characteristics associated with axial twisting introduced by knappers through the practice of beveling (LM3d1) (Selden Jr., Dockall, and Dubied 2020). The addition of cross-sections was needed to better characterise whole-object morphology, providing for the possibility of subsampling the landmarks to explore the contribution of a specific cross-section or profile (LM3d2). LM3d3 includes an additional cross section at the blade/base transition, allowing for tests of morphological integration. While true that some landmarking protocols can be—–and often are—–recycled as new specimens are added, this particular research programme endeavours to achieve ever-greater accuracy and precision in each analytical iteration.

Note: this landmarking protocol was developed prior to running auto3dgm, and details the procedure for applying landmarks and equidistant semilandmarks; however, it may not reflect their actual placement on this specimen.

Hypotheses

A suite of visual aids was created a means of visualising the various hypotheses that this landmarking protocol will be used to test. The visual representation of the following hypotheses were produced for my own reference, and used to critically assess the utility of the semilandmarks employed in the landmarking protocol. All hypotheses tested for this study will enlist the same sample of Dalton projectile points.

Hypothesis 1

Hypothesis 1 will test whether there is a difference in morphology for Dalton points found in and out of the heartland.

knitr::include_graphics('images/dalton-vizhypothesis1.jpg')

Hypothesis 1 considers whether Dalton points discovered in and out of the Heartland differ in morphology.

Hypothesis 2

Hypothesis 2 will test whether there is a difference in morphology for Dalton points found in the heartland, the interior, and the northern periphery.

knitr::include_graphics('images/dalton-vizhypothesis2.jpg')

Hypothesis 2 considers whether Dalton points discovered in the heartland, interior, and northern periphery differ in morphology.

Hypothesis 3

Hypothesis 3 will test whether there is a discernible difference in morphology for Dalton points that are beveled, or not beveled.

knitr::include_graphics('images/dalton-vizhypothesis3.jpg')

Hypothesis 3 considers whether beveled Dalton points differ in morphology from those that are not beveled.

Landmarking protocol 3d3

Generating the peripheral (plan view) spline

This effort begins with a spline extracted from the surface geometry of the mesh using the extract contour curves command. In reverse-engineering, extract contour curves is regularly employed as the first step in building a patch network used to create a surface. The extracted feature curve is rendered as a spline, and follows the highest curvature contours around the periphery of the lateral and basal edges, following the highly variable sinuous edge morphology around the entirety of the projectile. The remainder of the landmarking protocol is based upon this spline, which was subsequently split at six mathematically-defined locations.

knitr::include_graphics('images/extractspline.png')

Spline extracted along the highest contours of the Dalton point.

Splitting the spline

Reference geometries are used in the assistance of creating other features. These include basic geometric entities, such as planes, vectors, coordinates, points, and polygons. A reference point is a virtual point and is used to mark a specific position on a model or in 3D space. A reference plane is a virtual plane that has a normal direction and an infinite size. A reference plane is not a surface body, and is used to create other features.

The characteristic points and tangents developed for this landmarking protocol were inspired by the work of Birkhoff (1933), which has been gainfully employed within the context of both ceramic (Selden Jr. 2018a, 2018b, 2019, 2020) and lithic analyses (Selden Jr., Dockall, and Shafer 2018; Selden Jr., Dockall, and Dubied 2020). The first landmark (LM1) is placed at the horizontal tangent on the tip of each Dalton point. The second through fifth splits (LMs 02 - 05) occur at points of highest curvature, where LM 02 is always placed on the right side of the projectile when oriented in 3D space following the alignment output of auto3dgm. To place the final landmark (LM 06), a linear measurement was used to project a reference point equidistant between LM 02 and LM 03. The location of that point was leveraged in placing the reference plane used to cut the spline at the location of LM 06.

Spline split at location of LM 01

The horizontal tangent is calculated by drawing a horizontal line above the tip of the biface using the tangent as a common constraint, and the horizontal as the independent constraint. To split the 3D spline at the location of the horizontal tangent, a reference point was inserted at the location of the tangent in the sketch (light blue point; below, left), followed by a reference plane (in white; below, left and right) using the pick point and normal axis function where the reference point (h-tangent) was used as the pick point, and the Right plane as the normal axis (below, left). The spline was then cut at the location where the reference plane intersected with the spline (below image, right).

knitr::include_graphics('images/lm1.png')

Identify horizontal tangent, insert reference point and reference plane (left). Use reference plane to cut spline at the location of the horizontal tangent (right).

Spline split at locations of LM 02 - LM 03

The point of highest curvature on either side of the basal edge was calculated using the curvature function in the Accuracy Analyser. This function displays the curvature flow as a continuous colour plot across the area of the curve. In this instance, curvature is defined as the amount by which a geometric shape deviates from being flat or straight in the case of a line. The curvature is displayed in different colours according to the local radius, and is calculated in only one direction (U or V) along the curve. Using this tool, the two points of highest curvature were located between the basal and lateral edges on either side of each projectile where the local radius measure was largest. The alignment and orientation of each biface was dictated by the auto3dgm output, and the landmarking protocol follows the mesh orientation, where LM 02 was always placed on the right side of the basal edge, and LM 03 on the left.

knitr::include_graphics('images/splinesplit1.png')

Identify points of hightest curvature (light blue) at left/right intersection of lateral and basal edges.

Spline split at locations of LM 04 and LM 05

The point of highest curvature at the intersection of the blade and base was also calculated using the curvature function in the Accuracy Analyser. Using this tool, the two points of highest curvature were located between the blade and base on either side of each projectile where the local radius measure was largest. The alignment and orientation of each biface was dictated by the auto3dgm output, and the landmarking protocol follows the mesh orientation in that figure, where LM 04 was always placed on the right side of the basal edge, and LM 05 on the left.

knitr::include_graphics('images/splinesplit2.png')

Identify points of hightest curvature (light blue) at left/right intersection of blade and base.

Spline split at location of LM 06

One additional landmark (LM 06) was placed at the centre of the base. The location of this landmark was identified by calculating the linear distance between LM 02 and LM 03, and projecting a reference point (ctrl-div; below) equidistant between the two. A reference plane was added using the ctrl-div as the pick point, and the Right plane as the normal axis. The spline was then split at the intersection of the reference plane and the basal spline.

knitr::include_graphics('images/lm6.png')

Calculate linear distance between LM 02 and LM 03, insert reference plane coplanar to Right plane equidistant between LM 02 and LM 03, and use the reference plane to cut the spline.

Peripheral (plan view) spline

Through the preceding protocol, the initial spline was split into six discrete splines. These splines articulate with components of projectile morphology that can be compartmentalised in the analyses. The primary analytical gain achieved through this exercise is the requisite foundation needed to carry out replicable analyses of Dalton point morphology in three dimensions, further increasing the precision of the geometric morphometric analysis.

knitr::include_graphics('images/splinesplit-frbl.png')

Result of spline splits include six discrete splines, each articulating with a region of analytical interest.

Reference vectors

The fundamental components of reference geometry used to create LM3d2 are two reference vectors. The vectors were placed between LMs 01 and 06, and LMs 04 and 05, and serve as the basis for the remaining reference geometry needed to place the semilandmarks.

knitr::include_graphics('images/lm3d3.vectors.png')

Reference vectors placed between LMs 01 and 06 (left), and between LMs 04 and 05 (right).

Reference planes and points

Four reference planes provide the framework needed to populate the semilandmarks. Admittedly, the logic associated with placement may seem curious at this point; however, the utility of these reference planes will become clear in subsequent sections.

Placement of ref.pl.1

The first reference plane (ref.pl.1) was placed between LMs 01 and 06 in such a way that it bisects the projectile along the midline. The method of placement enlists a reference point (ref.pt.1), which was inserted along the first reference vector. It is located at a position equidistant between LMs 01 and 06, but the reference point coordinates were altered to relocate it 15 mm from the vector in the direction of the Z-axis. The pick point and coplanar function was used to place the plane coplanar to the first reference vector, and in the direction of ref.pt.1. Following placement of ref.pl.1, ref.pt.1 was deleted.

knitr::include_graphics('images/lm3d3.ref.pl.1.png')

Placement of ref.pl.1, and location of ref.pt.1.

Placement of ref.pl.2

The second reference plane (ref.pl.2) was placed between LMs 04 and 05, and bisects the projectile at the blade/base intersection. The method of placement for ref.pl.2 follows the same protocol described in the previous section, and the reference point (ref.pt.2) was deleted following the placement of ref.pl.2.

knitr::include_graphics('images/lm3d3.ref.pl.2.png')

Placement of ref.pl.2, and location of ref.pt.2.

Placement of ref.pl.3 and ref.pl.4

The third (ref.pl.3) and fourth (ref.pl.4) reference planes were placed using the pick point and normal function at the intersections of the first reference vector and LMs 01 and 06.

knitr::include_graphics('images/lm3d3.ref.pl.3-4.png')

Placement of ref.pl.3 (top) and ref.pl.4 (bottom).

Sectioning the mesh

The reference geometry described above was enlisted in the following three-step method developed to produce one cross-section at the blade/base intersection, four cross-sections between the blade/base intersection and LM 01, and one cross-section between the blade/base intersection and LM 06, to include one that articulates with the location of LM 06.

Sectioning the blade/base intersection

To section the blade/base intersection, a single section was inserted using ref.pl.2, resulting in a single cross-section that bisects the projectile between LMs 04 and 05.

knitr::include_graphics('images/lm3d3.section1.png')

Placement of the first section, bisecting the mesh along ref.pl.2.

Sectioning the blade and base

A single reference point (ref.pt.3) was placed equidistant along the reference vector between LMs 04 and 05. Six equidistant sections were placed between LM 01 and ref.pt.3, and the two sections at the locations of LM 01 and ref.pt.3 were deleted. Three equidistant sections were placed between LM 06 and ref.pt.3. The section intersecting with ref.pt.3 was deleted. Subsequent to placing the sections, ref.pt.3 was itself deleted.

knitr::include_graphics('images/lm3d3.all.sections.png')

Placement of the two equidistant sections between LM 06 and ref.pt.3.

Splitting the sections

The curvature function was employed to split the spline at the location of highest curvature. This function was detailed in the application of LMs 02, 03, 04, and 05 in LM3d1. Each section was split at the point of highest curvature along the lateral margins. The reference plane ref.pl.1 was then used to cut each curve along the mid-line where it intersects with the curves.

knitr::include_graphics('images/lm3d3.split.sections.png')

Each section was split at the points of highest curvature along the lateral edges, then along the mid-line at the intersection of the curve and ref.pl.1.

Applying the semilandmarks

Semilandmarks 07 - 20 were first applied around the lateral edges, and sLMs 13 and 14 between LMs 02, 06, and 03 uses the curve constructed in LM3d1. Semilandmarks 21 - 32 articulate with the mid-line between LMs 01 and 06. Additional sLMs (33 - 57) were placed on each section equidistant between those sLMs defined by the splits described above.

The result is a landmark configuration that can be subset in numerous ways (plan, profile, cross-section, front/back, left/right, blade/base, etc.), and was designed to achieve maximum utility for analysts of lithic morphology.

knitr::include_graphics('images/lm3d3.semi.png')

Landmarks (blue), semilandmarks (white), curves (orange), and splits (blue) used for LM3d3.

Based upon knowledge garnered from running LaSEC on LM3d1, this landmarking protocol is likely oversampled; however, it can be further modified or subsampled to include only those landmarks and semilandmarks needed to address the research question.

knitr::include_graphics('images/lm3d3.slm.png')

Landmarks (blue), semilandmarks (white), and reference geometry used in LM3d3.

Acknowledgments

I extend my gratitude to Christian S. Hoggard and David K. Thulman for their thoughtful comments and constructive criticisms on the draft of this landmarking protocol, which was originally developed for the study of Gahagan bifaces (Selden Jr., Dockall, and Dubied 2020), and is extended here for an analysis of Dalton point morphology. This iteration of the landmarking protocol was developed using the digit3DLand package in R.

Birkhoff, George D. 1933. Aesthetic Measure. Cambridge: Harvard University Press.

Selden Jr., Robert Z. 2018a. “A Preliminary Study of Smithport Plain Bottle Morphology in the Southern Caddo Area.” Bulletin of the Texas Archeological Society 89: 63–89.

———. 2018b. “Ceramic Morphological Organisation in the Southern Caddo Area: Quiddity of Shape for Hickory Engraved Bottles.” Journal of Archaeological Science: Reports 21: 884–96. https://doi.org/10.1016/j.jasrep.2018.08.045.

———. 2019. “Ceramic Morphological Organisation in the Southern Caddo Area: The Clarence H. Webb Collections.” Journal of Cultural Heritage 35: 41–55. https://doi.org/https://doi.org/10.1016/j.culher.2018.07.002.

———. 2020. “Louisiana Limitrophe: An Iterative Morphological Exegesis of Caddo Bottle and Biface Production.” In Ancestral Caddo Ceramic Traditions, edited by Duncan P. McKinnon, Jeffrey S. Girard, and Timothy K. Perttula, (in press). Baton Rouge: LSU Press.

Selden Jr., Robert Z., John E. Dockall, and Morgane Dubied. 2020. “A Quantitative Assessment of Intraspecific Morphological Variation in Gahagan Bifaces from the Southern Caddo Area and Central Texas.” Southeastern Archaeology 39 (2): 125–45. https://doi.org/10.1080/0734578x.2020.1744416.

Selden Jr., Robert Z., John E. Dockall, and Harry J. Shafer. 2018. “Lithic Morphological Organisation: Gahagan Bifaces from the Southern Caddo Area.” Digital Applications in Archaeology and Cultural Heritage 10: e00080. https://doi.org/10.1016/j.daach.2018.e00080.